Set a fine-mesh strainer over a medium heatproof bowl next to the stove. In a heavy, medium saucepan, whisk together the sugar, lemon juice, eggs, egg yolks and lemon peel. Add the butter and cook over medium-low heat, stirring constantly, for 5 minutes.
Lower the heat and simmer, stirring, until the mixture thickens and registers 160 degrees on an instant-read thermometer, about 5 minutes. Strain the mixture into the prepared bowl, then press a sheet of plastic wrap directly onto the surface. Let cool to room temperature. Transfer to an airtight container and refrigerate for up to 1 month.
